欢乐MBA-F检验（总体方差差异和标准差接近）第十章

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[size=14.6667px]10.80 Two professors wanted to study how students from

[size=14.6667px]their two universities compared in their capabilities of using

[size=14.6667px]Excel spreadsheets in undergraduate information systems

[size=14.6667px]courses. (Data extracted from H. Howe and M. G. Simkin,

[size=14.6667px]“Factors Affecting the Ability to Detect Spreadsheet Errors,”

[size=14.6667px]Decision Sciences Journal of Innovative Education, January

[size=14.6667px]2006, pp. 101–122.) A comparison of the student demo-

[size=14.6667px]graphics was also performed. One school is a state university

[size=14.6667px]in the western United States, and the other school is a state

[size=14.6667px]university in the eastern United States. The following table

contains information regarding the ages of the students:

[size=14.6667px]School      [size=14.6667px]Sample [size=14.6667px]Size    Mean    [size=14.6667px]Standard [size=14.6667px]Deviation

[size=14.6667px]Western    93                    23.28          6.29

[size=14.6667px]Eastern    135                   21.16          1.32

[size=14.6667px]a. Using a 0.01 level of significance, is there evidence of a

[size=14.6667px]difference in the variances of the age of students at the

[size=14.6667px]western school and at the eastern school?

[size=14.6667px]（总体方差差异判断）

[size=14.6667px]

Solution：

H0 is σ1方=σ2方

H1 is [size=14.6667px]σ1方≠σ2方

FindF critical value for α=0.01

Numerator分子 df=92

Dominator分母 df=134

Fα/2=F0.01,92,134=1.32

FSTAT=s1方/s2方=大的方差/小的方差

=(6.29^(2))/(1.32^(2))=22.706669

1.31<1.32, we shouldreject H0, the variances of the age of students at thewestern school and at the eastern school should not be the same.

[size=14.6667px]The following table contains information regarding the

[size=14.6667px]years of spreadsheet usage of the students:

[size=14.6667px]School     [size=14.6667px]Sample [size=14.6667px]Size       Mean      [size=14.6667px]Standard[size=14.6667px]Deviation

[size=14.6667px]Western      93                      2.6                2.4

[size=14.6667px]Eastern      135                     4.0                2.1

[size=14.6667px]d. Using a 0.01 level of significance, is there evidence of a dif-

[size=14.6667px]ference in the variances of the years of spreadsheet usage of

[size=14.6667px]students at the western school and at the eastern school?

[size=14.6667px]e. Based on the results of (d), use the most appropriate test

[size=14.6667px]to determine, at the 0.01 level of significance, whether

[size=14.6667px]there is evidence of a difference in the mean years of

[size=14.6667px]spreadsheet usage of students at the western school and

[size=14.6667px]at the eastern school.

[size=14.6667px]（总体标准差接近相等且未知）

Pooled-variancet test should be used,

Assume

H0 is μ1=μ2

H1 is μ1≠μ2

Findcritical value tα/2=2.5758 when α=0.01

=4.9596

=-4.6649<-2.5758

So we could reject H0, theyare not equal.

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关键词：总体方差 标准差 F检验 Spreadsheets significance